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source: palm/trunk/SOURCE/lpm_advec.f90 @ 3271

Last change on this file since 3271 was 3241, checked in by raasch, 6 years ago
various changes to avoid compiler warnings (mainly removal of unused variables)
Property svn:keywords set to `Id`
File size: 54.9 KB

Rev	Line
[1682]	1	!> @file lpm_advec.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[849]	20	! Current revisions:
	21	! ------------------
[2701]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_advec.f90 3241 2018-09-12 15:02:00Z suehring $
[3241]	27	! unused variables removed
	28	!
	29	! 3207 2018-08-27 12:55:33Z schwenkel
[3207]	30	! Minor bugfix for sgs-velocities in case of cloud droplets
	31	!
	32	! 3189 2018-08-06 13:18:55Z raasch
[3189]	33	! Bugfix: Index of the array dzw has to be k+1 during the interpolation.
	34	! Otherwise k=0 causes an abortion because dzw is allocated from 1 to nzt+1
	35	!
	36	! 3065 2018-06-12 07:03:02Z Giersch
[3065]	37	! dz values were replaced by dzw or dz(1) to allow for right vertical stretching
	38	!
	39	! 2969 2018-04-13 11:55:09Z thiele
[2969]	40	! Bugfix in Interpolation indices.
	41	!
	42	! 2886 2018-03-14 11:51:53Z thiele
[2886]	43	! Bugfix in passive particle SGS Model:
	44	! Sometimes the added SGS velocities would lead to a violation of the CFL
	45	! criterion for single particles. For this a check was added after the
	46	! calculation of SGS velocities.
	47	!
	48	! 2718 2018-01-02 08:49:38Z maronga
[2716]	49	! Corrected "Former revisions" section
	50	!
	51	! 2701 2017-12-15 15:40:50Z suehring
	52	! Changes from last commit documented
	53	!
	54	! 2698 2017-12-14 18:46:24Z suehring
[2698]	55	! Particle interpolations at walls in case of SGS velocities revised and not
	56	! required parts are removed. (responsible Philipp Thiele)
[2716]	57	! Bugfix in get_topography_top_index
[2698]	58	!
[2716]	59	! 2696 2017-12-14 17:12:51Z kanani
	60	! Change in file header (GPL part)
	61	!
	62	! 2630 2017-11-20 12:58:20Z schwenkel
[2629]	63	! Removed indices ilog and jlog which are no longer needed since particle box
	64	! locations are identical to scalar boxes and topography.
	65	!
[2630]	66	! 2628 2017-11-20 12:40:38Z raasch
[2610]	67	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
	68	!
	69	! 2606 2017-11-10 10:36:31Z schwenkel
[2606]	70	! Changed particle box locations: center of particle box now coincides
	71	! with scalar grid point of same index.
	72	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
	73	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
	74	! lpm_sort -> lpm_sort_timeloop_done
	75	!
	76	! 2417 2017-09-06 15:22:27Z suehring
[2417]	77	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
	78	! particle loop runs from start_index up to end_index instead from 1 to
	79	! number_of_particles. This way, it is possible to skip unnecessary
	80	! computations for particles that already completed the LES timestep.
	81	!
	82	! 2318 2017-07-20 17:27:44Z suehring
[2318]	83	! Get topography top index via Function call
	84	!
	85	! 2317 2017-07-20 17:27:19Z suehring
[1930]	86	!
[2233]	87	! 2232 2017-05-30 17:47:52Z suehring
	88	! Adjustments to new topography and surface concept
	89	!
[2101]	90	! 2100 2017-01-05 16:40:16Z suehring
	91	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
	92	! at the begin of simulations and/or in non-turbulent regions.
	93	!
[2001]	94	! 2000 2016-08-20 18:09:15Z knoop
	95	! Forced header and separation lines into 80 columns
	96	!
[1937]	97	! 1936 2016-06-13 13:37:44Z suehring
	98	! Formatting adjustments
	99	!
[1930]	100	! 1929 2016-06-09 16:25:25Z suehring
[1929]	101	! Put stochastic equation in an extra subroutine.
	102	! Set flag for stochastic equation to communicate whether a particle is near
	103	! topography. This case, memory and drift term are disabled in the Weil equation.
[1889]	104	!
[1929]	105	! Enable vertical logarithmic interpolation also above topography. This case,
	106	! set a lower limit for the friction velocity, as it can become very small
[1930]	107	! in narrow street canyons, leading to too large particle speeds.
[1823]	108	!
[1889]	109	! 1888 2016-04-21 12:20:49Z suehring
	110	! Bugfix concerning logarithmic interpolation of particle speed
	111	!
[1823]	112	! 1822 2016-04-07 07:49:42Z hoffmann
[1822]	113	! Random velocity fluctuations for particles added. Terminal fall velocity
	114	! for droplets is calculated from a parameterization (which is better than
	115	! the previous, physically correct calculation, which demands a very short
	116	! time step that is not used in the model).
	117	!
	118	! Unused variables deleted.
[1321]	119	!
[1692]	120	! 1691 2015-10-26 16:17:44Z maronga
	121	! Renamed prandtl_layer to constant_flux_layer.
	122	!
[1686]	123	! 1685 2015-10-08 07:32:13Z raasch
	124	! TKE check for negative values (so far, only zero value was checked)
	125	! offset_ocean_nzt_m1 removed
	126	!
[1683]	127	! 1682 2015-10-07 23:56:08Z knoop
	128	! Code annotations made doxygen readable
	129	!
[1584]	130	! 1583 2015-04-15 12:16:27Z suehring
	131	! Bugfix: particle advection within Prandtl-layer in case of Galilei
	132	! transformation.
	133	!
[1370]	134	! 1369 2014-04-24 05:57:38Z raasch
	135	! usage of module interfaces removed
	136	!
[1360]	137	! 1359 2014-04-11 17:15:14Z hoffmann
	138	! New particle structure integrated.
	139	! Kind definition added to all floating point numbers.
	140	!
[1323]	141	! 1322 2014-03-20 16:38:49Z raasch
	142	! REAL constants defined as wp_kind
	143	!
[1321]	144	! 1320 2014-03-20 08:40:49Z raasch
[1320]	145	! ONLY-attribute added to USE-statements,
	146	! kind-parameters added to all INTEGER and REAL declaration statements,
	147	! kinds are defined in new module kinds,
	148	! revision history before 2012 removed,
	149	! comment fields (!:) to be used for variable explanations added to
	150	! all variable declaration statements
[849]	151	!
[1315]	152	! 1314 2014-03-14 18:25:17Z suehring
	153	! Vertical logarithmic interpolation of horizontal particle speed for particles
	154	! between roughness height and first vertical grid level.
	155	!
[1037]	156	! 1036 2012-10-22 13:43:42Z raasch
	157	! code put under GPL (PALM 3.9)
	158	!
[850]	159	! 849 2012-03-15 10:35:09Z raasch
	160	! initial revision (former part of advec_particles)
[849]	161	!
[850]	162	!
[849]	163	! Description:
	164	! ------------
[1682]	165	!> Calculation of new particle positions due to advection using a simple Euler
	166	!> scheme. Particles may feel inertia effects. SGS transport can be included
	167	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
[849]	168	!------------------------------------------------------------------------------!
[1682]	169	SUBROUTINE lpm_advec (ip,jp,kp)
	170
[849]	171
[1320]	172	USE arrays_3d, &
[3065]	173	ONLY: de_dx, de_dy, de_dz, diss, dzw, e, km, u, v, w, zu, zw
[849]	174
[1359]	175	USE cpulog
	176
	177	USE pegrid
	178
[1320]	179	USE control_parameters, &
[3241]	180	ONLY: cloud_droplets, constant_flux_layer, dt_3d, dt_3d_reached_l, &
	181	dz, g, kappa, topography, u_gtrans, v_gtrans
[849]	182
[1320]	183	USE grid_variables, &
[3241]	184	ONLY: dx, dy
[1320]	185
	186	USE indices, &
[2698]	187	ONLY: nzb, nzt, wall_flags_0
[1320]	188
	189	USE kinds
	190
	191	USE particle_attributes, &
[3241]	192	ONLY: block_offset, c_0, dt_min_part, grid_particles, iran_part, &
	193	log_z_z0, number_of_particles, number_of_sublayers, &
	194	particles, particle_groups, sgs_wf_part, &
[1929]	195	use_sgs_for_particles, vertical_particle_advection, z0_av_global
[1320]	196
	197	USE statistics, &
	198	ONLY: hom
[849]	199
[2232]	200	USE surface_mod, &
[2698]	201	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
[2232]	202
[1320]	203	IMPLICIT NONE
[849]	204
[2698]	205	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
	206
[1929]	207	INTEGER(iwp) :: i !< index variable along x
	208	INTEGER(iwp) :: ip !< index variable along x
	209	INTEGER(iwp) :: j !< index variable along y
	210	INTEGER(iwp) :: jp !< index variable along y
	211	INTEGER(iwp) :: k !< index variable along z
[2232]	212	INTEGER(iwp) :: k_wall !< vertical index of topography top
[1929]	213	INTEGER(iwp) :: kp !< index variable along z
	214	INTEGER(iwp) :: kw !< index variable along z
	215	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
	216	INTEGER(iwp) :: nb !< block number particles are sorted in
[2232]	217	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
[849]	218
[1929]	219	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
	220	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
[1359]	221
[1929]	222	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
	223	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
	224	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
	225	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
	226	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
	227	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
	228	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
	229	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
	230	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
	231	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
	232	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
	233	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
	234	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
[1822]	235	REAL(wp) :: diameter !< diamter of droplet
[1929]	236	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
	237	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
	238	REAL(wp) :: dt_particle_m !< previous particle time step
[2886]	239	REAL(wp) :: dz_temp !<
[1929]	240	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
	241	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
	242	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
[1682]	243	REAL(wp) :: exp_arg !<
	244	REAL(wp) :: exp_term !<
[1929]	245	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
	246	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
	247	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
[1682]	248	REAL(wp) :: random_gauss !<
[1822]	249	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
	250	REAL(wp) :: rg1 !< Gaussian distributed random number
	251	REAL(wp) :: rg2 !< Gaussian distributed random number
	252	REAL(wp) :: rg3 !< Gaussian distributed random number
	253	REAL(wp) :: sigma !< velocity standard deviation
[1929]	254	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
	255	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
	256	REAL(wp) :: us_int !< friction velocity at particle grid box
[2232]	257	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
[1929]	258	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
	259	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
[2232]	260	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
[1682]	261	REAL(wp) :: vv_int !<
[1929]	262	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
	263	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
[1822]	264	REAL(wp) :: w_s !< terminal velocity of droplets
[1929]	265	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
	266	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
	267	REAL(wp) :: z_p !< surface layer height (0.5 dz)
[849]	268
[1822]	269	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
	270	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
	271	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
	272	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
	273	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
	274	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
	275
[2886]	276	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
	277	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !<
	278	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
	279	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
	280	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
	281	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
	282	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
	283	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
	284	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
	285	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
	286	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
	287	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !<
	288	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !<
	289	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !<
	290	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
	291	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
	292	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
	293	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
	294	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
	295	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
[1359]	296
[1929]	297	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
[1359]	298
	299	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
	300
[1314]	301	!
	302	!-- Determine height of Prandtl layer and distance between Prandtl-layer
	303	!-- height and horizontal mean roughness height, which are required for
	304	!-- vertical logarithmic interpolation of horizontal particle speeds
	305	!-- (for particles below first vertical grid level).
	306	z_p = zu(nzb+1) - zw(nzb)
[1359]	307	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
[849]	308
[1359]	309	start_index = grid_particles(kp,jp,ip)%start_index
	310	end_index = grid_particles(kp,jp,ip)%end_index
[849]	311
[1359]	312	xv = particles(1:number_of_particles)%x
	313	yv = particles(1:number_of_particles)%y
	314	zv = particles(1:number_of_particles)%z
[849]	315
[1359]	316	DO nb = 0, 7
[2606]	317	!
	318	!-- Interpolate u velocity-component
[1359]	319	i = ip
	320	j = jp + block_offset(nb)%j_off
	321	k = kp + block_offset(nb)%k_off
[2606]	322
[1359]	323	DO n = start_index(nb), end_index(nb)
[1314]	324	!
[1359]	325	!-- Interpolation of the u velocity component onto particle position.
	326	!-- Particles are interpolation bi-linearly in the horizontal and a
	327	!-- linearly in the vertical. An exception is made for particles below
	328	!-- the first vertical grid level in case of a prandtl layer. In this
	329	!-- case the horizontal particle velocity components are determined using
	330	!-- Monin-Obukhov relations (if branch).
	331	!-- First, check if particle is located below first vertical grid level
[2232]	332	!-- above topography (Prandtl-layer height)
	333	!-- Determine vertical index of topography top
[2698]	334	k_wall = get_topography_top_index_ji( jp, ip, 's' )
[1929]	335
[2232]	336	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
[1314]	337	!
[1359]	338	!-- Resolved-scale horizontal particle velocity is zero below z0.
[2232]	339	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1359]	340	u_int(n) = 0.0_wp
	341	ELSE
[1314]	342	!
[1359]	343	!-- Determine the sublayer. Further used as index.
[2232]	344	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	345	* REAL( number_of_sublayers, KIND=wp ) &
[1359]	346	* d_z_p_z0
[1314]	347	!
[1359]	348	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	349	!-- interpolate linearly between precalculated logarithm.
[1929]	350	log_z_z0_int = log_z_z0(INT(height_p)) &
[1359]	351	+ ( height_p - INT(height_p) ) &
	352	* ( log_z_z0(INT(height_p)+1) &
	353	- log_z_z0(INT(height_p)) &
	354	)
[1314]	355	!
[2232]	356	!-- Get friction velocity and momentum flux from new surface data
	357	!-- types.
[2628]	358	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	359	surf_def_h(0)%end_index(jp,ip) ) THEN
	360	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	361	!-- Limit friction velocity. In narrow canyons or holes the
	362	!-- friction velocity can become very small, resulting in a too
	363	!-- large particle speed.
	364	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
	365	usws_int = surf_def_h(0)%usws(surf_start)
[2628]	366	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	367	surf_lsm_h%end_index(jp,ip) ) THEN
	368	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	369	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
	370	usws_int = surf_lsm_h%usws(surf_start)
[2628]	371	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	372	surf_usm_h%end_index(jp,ip) ) THEN
	373	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	374	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
	375	usws_int = surf_usm_h%usws(surf_start)
	376	ENDIF
	377
[1929]	378	!
[1359]	379	!-- Neutral solution is applied for all situations, e.g. also for
	380	!-- unstable and stable situations. Even though this is not exact
	381	!-- this saves a lot of CPU time since several calls of intrinsic
	382	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	383	!-- as sensitivity studies revealed no significant effect of
	384	!-- using the neutral solution also for un/stable situations.
[2232]	385	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	386	* log_z_z0_int - u_gtrans
	387
[1359]	388	ENDIF
	389	!
	390	!-- Particle above the first grid level. Bi-linear interpolation in the
	391	!-- horizontal and linear interpolation in the vertical direction.
[1314]	392	ELSE
	393
[2969]	394	x = xv(n) - i * dx
	395	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	396	aa = x2 + y2
	397	bb = ( dx - x )2 + y2
	398	cc = x2 + ( dy - y )2
	399	dd = ( dx - x )2 + ( dy - y )2
	400	gg = aa + bb + cc + dd
[1314]	401
[1359]	402	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
	403	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
	404	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[1314]	405
[1359]	406	IF ( k == nzt ) THEN
	407	u_int(n) = u_int_l
	408	ELSE
	409	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
	410	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
	411	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[3189]	412	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	413	( u_int_u - u_int_l )
	414	ENDIF
[1929]	415
[1314]	416	ENDIF
	417
[1359]	418	ENDDO
[2606]	419	!
	420	!-- Same procedure for interpolation of the v velocity-component
[1359]	421	i = ip + block_offset(nb)%i_off
	422	j = jp
	423	k = kp + block_offset(nb)%k_off
[2606]	424
[1359]	425	DO n = start_index(nb), end_index(nb)
[1685]	426
[2232]	427	!
	428	!-- Determine vertical index of topography top
[2698]	429	k_wall = get_topography_top_index_ji( jp,ip, 's' )
[849]	430
[2232]	431	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
	432	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1314]	433	!
[1359]	434	!-- Resolved-scale horizontal particle velocity is zero below z0.
	435	v_int(n) = 0.0_wp
	436	ELSE
	437	!
[1929]	438	!-- Determine the sublayer. Further used as index. Please note,
	439	!-- logarithmus can not be reused from above, as in in case of
	440	!-- topography particle on u-grid can be above surface-layer height,
	441	!-- whereas it can be below on v-grid.
[2232]	442	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	443	* REAL( number_of_sublayers, KIND=wp ) &
[1929]	444	* d_z_p_z0
	445	!
	446	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	447	!-- interpolate linearly between precalculated logarithm.
	448	log_z_z0_int = log_z_z0(INT(height_p)) &
	449	+ ( height_p - INT(height_p) ) &
	450	* ( log_z_z0(INT(height_p)+1) &
	451	- log_z_z0(INT(height_p)) &
	452	)
	453	!
[2232]	454	!-- Get friction velocity and momentum flux from new surface data
	455	!-- types.
[2628]	456	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	457	surf_def_h(0)%end_index(jp,ip) ) THEN
	458	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	459	!-- Limit friction velocity. In narrow canyons or holes the
	460	!-- friction velocity can become very small, resulting in a too
	461	!-- large particle speed.
	462	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
[2610]	463	vsws_int = surf_def_h(0)%vsws(surf_start)
[2628]	464	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	465	surf_lsm_h%end_index(jp,ip) ) THEN
	466	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	467	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
[2610]	468	vsws_int = surf_lsm_h%vsws(surf_start)
[2628]	469	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	470	surf_usm_h%end_index(jp,ip) ) THEN
	471	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	472	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
[2610]	473	vsws_int = surf_usm_h%vsws(surf_start)
[2232]	474	ENDIF
[1929]	475	!
[1359]	476	!-- Neutral solution is applied for all situations, e.g. also for
	477	!-- unstable and stable situations. Even though this is not exact
	478	!-- this saves a lot of CPU time since several calls of intrinsic
	479	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	480	!-- as sensitivity studies revealed no significant effect of
	481	!-- using the neutral solution also for un/stable situations.
[2232]	482	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	483	* log_z_z0_int - v_gtrans
[1314]	484
[1359]	485	ENDIF
[1929]	486
[1359]	487	ELSE
[2969]	488	x = xv(n) + ( 0.5_wp - i ) * dx
	489	y = yv(n) - j * dy
[1359]	490	aa = x2 + y2
	491	bb = ( dx - x )2 + y2
	492	cc = x2 + ( dy - y )2
	493	dd = ( dx - x )2 + ( dy - y )2
	494	gg = aa + bb + cc + dd
[1314]	495
[1359]	496	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
	497	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
	498	) / ( 3.0_wp * gg ) - v_gtrans
[1314]	499
[1359]	500	IF ( k == nzt ) THEN
	501	v_int(n) = v_int_l
	502	ELSE
	503	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
	504	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
	505	) / ( 3.0_wp * gg ) - v_gtrans
[3189]	506	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	507	( v_int_u - v_int_l )
	508	ENDIF
[1929]	509
[1314]	510	ENDIF
	511
[1359]	512	ENDDO
[2606]	513	!
	514	!-- Same procedure for interpolation of the w velocity-component
[1359]	515	i = ip + block_offset(nb)%i_off
	516	j = jp + block_offset(nb)%j_off
[1929]	517	k = kp - 1
[2606]	518
[1359]	519	DO n = start_index(nb), end_index(nb)
[849]	520
[1359]	521	IF ( vertical_particle_advection(particles(n)%group) ) THEN
[849]	522
[2969]	523	x = xv(n) + ( 0.5_wp - i ) * dx
	524	y = yv(n) + ( 0.5_wp - j ) * dy
[849]	525	aa = x2 + y2
	526	bb = ( dx - x )2 + y2
	527	cc = x2 + ( dy - y )2
	528	dd = ( dx - x )2 + ( dy - y )2
	529	gg = aa + bb + cc + dd
	530
[1359]	531	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
	532	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
	533	) / ( 3.0_wp * gg )
[849]	534
[1359]	535	IF ( k == nzt ) THEN
	536	w_int(n) = w_int_l
[849]	537	ELSE
[1359]	538	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
	539	( gg-bb ) * w(k+1,j,i+1) + &
	540	( gg-cc ) * w(k+1,j+1,i) + &
	541	( gg-dd ) * w(k+1,j+1,i+1) &
	542	) / ( 3.0_wp * gg )
[3189]	543	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
[1359]	544	( w_int_u - w_int_l )
[849]	545	ENDIF
	546
[1359]	547	ELSE
[849]	548
[1359]	549	w_int(n) = 0.0_wp
[849]	550
[1359]	551	ENDIF
	552
	553	ENDDO
	554
	555	ENDDO
	556
	557	!-- Interpolate and calculate quantities needed for calculating the SGS
	558	!-- velocities
[1822]	559	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[2698]	560
	561	DO nb = 0,7
	562
	563	subbox_at_wall = .FALSE.
	564	!
	565	!-- In case of topography check if subbox is adjacent to a wall
	566	IF ( .NOT. topography == 'flat' ) THEN
	567	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
	568	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
	569	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
	570	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
	571	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
	572	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
	573	THEN
	574	subbox_at_wall = .TRUE.
	575	ENDIF
	576	ENDIF
	577	IF ( subbox_at_wall ) THEN
	578	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
	579	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
	580	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
	581	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
	582	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
	583	!
	584	!-- Set flag for stochastic equation.
	585	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
	586	ELSE
[1359]	587	i = ip + block_offset(nb)%i_off
	588	j = jp + block_offset(nb)%j_off
	589	k = kp + block_offset(nb)%k_off
	590
	591	DO n = start_index(nb), end_index(nb)
[849]	592	!
[1359]	593	!-- Interpolate TKE
[2969]	594	x = xv(n) + ( 0.5_wp - i ) * dx
	595	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	596	aa = x2 + y2
	597	bb = ( dx - x )2 + y2
	598	cc = x2 + ( dy - y )2
	599	dd = ( dx - x )2 + ( dy - y )2
	600	gg = aa + bb + cc + dd
[849]	601
[1359]	602	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
	603	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
	604	) / ( 3.0_wp * gg )
	605
	606	IF ( k+1 == nzt+1 ) THEN
	607	e_int(n) = e_int_l
	608	ELSE
	609	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
	610	( gg - bb ) * e(k+1,j,i+1) + &
	611	( gg - cc ) * e(k+1,j+1,i) + &
	612	( gg - dd ) * e(k+1,j+1,i+1) &
	613	) / ( 3.0_wp * gg )
[3189]	614	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	615	( e_int_u - e_int_l )
	616	ENDIF
[849]	617	!
[1685]	618	!-- Needed to avoid NaN particle velocities (this might not be
	619	!-- required any more)
	620	IF ( e_int(n) <= 0.0_wp ) THEN
[1359]	621	e_int(n) = 1.0E-20_wp
	622	ENDIF
	623	!
	624	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
	625	!-- all position variables from above (TKE))
	626	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
	627	( gg - bb ) * de_dx(k,j,i+1) + &
	628	( gg - cc ) * de_dx(k,j+1,i) + &
	629	( gg - dd ) * de_dx(k,j+1,i+1) &
	630	) / ( 3.0_wp * gg )
[849]	631
	632	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
[1359]	633	de_dx_int(n) = de_dx_int_l
[849]	634	ELSE
[1359]	635	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
	636	( gg - bb ) * de_dx(k+1,j,i+1) + &
	637	( gg - cc ) * de_dx(k+1,j+1,i) + &
	638	( gg - dd ) * de_dx(k+1,j+1,i+1) &
	639	) / ( 3.0_wp * gg )
[3189]	640	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	641	( de_dx_int_u - de_dx_int_l )
[849]	642	ENDIF
[1359]	643	!
	644	!-- Interpolate the TKE gradient along y
	645	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
	646	( gg - bb ) * de_dy(k,j,i+1) + &
	647	( gg - cc ) * de_dy(k,j+1,i) + &
	648	( gg - dd ) * de_dy(k,j+1,i+1) &
	649	) / ( 3.0_wp * gg )
	650	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	651	de_dy_int(n) = de_dy_int_l
	652	ELSE
	653	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
[2698]	654	( gg - bb ) * de_dy(k+1,j,i+1) + &
	655	( gg - cc ) * de_dy(k+1,j+1,i) + &
	656	( gg - dd ) * de_dy(k+1,j+1,i+1) &
[1359]	657	) / ( 3.0_wp * gg )
[3189]	658	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	659	( de_dy_int_u - de_dy_int_l )
[1359]	660	ENDIF
[849]	661
	662	!
[1359]	663	!-- Interpolate the TKE gradient along z
[3065]	664	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
[1359]	665	de_dz_int(n) = 0.0_wp
	666	ELSE
	667	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
	668	( gg - bb ) * de_dz(k,j,i+1) + &
	669	( gg - cc ) * de_dz(k,j+1,i) + &
	670	( gg - dd ) * de_dz(k,j+1,i+1) &
	671	) / ( 3.0_wp * gg )
[849]	672
[1359]	673	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	674	de_dz_int(n) = de_dz_int_l
	675	ELSE
	676	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
	677	( gg - bb ) * de_dz(k+1,j,i+1) + &
	678	( gg - cc ) * de_dz(k+1,j+1,i) + &
	679	( gg - dd ) * de_dz(k+1,j+1,i+1) &
	680	) / ( 3.0_wp * gg )
[3189]	681	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	682	( de_dz_int_u - de_dz_int_l )
	683	ENDIF
	684	ENDIF
[849]	685
[1359]	686	!
	687	!-- Interpolate the dissipation of TKE
	688	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
	689	( gg - bb ) * diss(k,j,i+1) + &
	690	( gg - cc ) * diss(k,j+1,i) + &
	691	( gg - dd ) * diss(k,j+1,i+1) &
[2698]	692	) / ( 3.0_wp * gg )
[849]	693
[1359]	694	IF ( k == nzt ) THEN
	695	diss_int(n) = diss_int_l
	696	ELSE
	697	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
	698	( gg - bb ) * diss(k+1,j,i+1) + &
	699	( gg - cc ) * diss(k+1,j+1,i) + &
	700	( gg - dd ) * diss(k+1,j+1,i+1) &
	701	) / ( 3.0_wp * gg )
[3189]	702	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	703	( diss_int_u - diss_int_l )
[1359]	704	ENDIF
	705
[1929]	706	!
	707	!-- Set flag for stochastic equation.
	708	term_1_2(n) = 1.0_wp
[1359]	709	ENDDO
[2698]	710	ENDIF
	711	ENDDO
[1359]	712
	713	DO nb = 0,7
	714	i = ip + block_offset(nb)%i_off
	715	j = jp + block_offset(nb)%j_off
	716	k = kp + block_offset(nb)%k_off
[849]	717
[1359]	718	DO n = start_index(nb), end_index(nb)
[849]	719	!
[1359]	720	!-- Vertical interpolation of the horizontally averaged SGS TKE and
	721	!-- resolved-scale velocity variances and use the interpolated values
	722	!-- to calculate the coefficient fs, which is a measure of the ratio
	723	!-- of the subgrid-scale turbulent kinetic energy to the total amount
	724	!-- of turbulent kinetic energy.
	725	IF ( k == 0 ) THEN
	726	e_mean_int = hom(0,1,8,0)
	727	ELSE
	728	e_mean_int = hom(k,1,8,0) + &
	729	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
	730	( zu(k+1) - zu(k) ) * &
	731	( zv(n) - zu(k) )
	732	ENDIF
[849]	733
[1685]	734	kw = kp - 1
[849]	735
[1359]	736	IF ( k == 0 ) THEN
	737	aa = hom(k+1,1,30,0) * ( zv(n) / &
	738	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	739	bb = hom(k+1,1,31,0) * ( zv(n) / &
	740	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	741	cc = hom(kw+1,1,32,0) * ( zv(n) / &
	742	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
	743	ELSE
	744	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
	745	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	746	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
	747	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	748	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
	749	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
	750	ENDIF
[849]	751
[1359]	752	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
	753	!
	754	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
	755	!-- an educated guess for the given case.
	756	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
	757	fs_int(n) = 1.0_wp
	758	ELSE
	759	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
	760	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
	761	ENDIF
[849]	762
[1359]	763	ENDDO
	764	ENDDO
[849]	765
[2417]	766	DO nb = 0, 7
	767	DO n = start_index(nb), end_index(nb)
	768	rg(n,1) = random_gauss( iran_part, 5.0_wp )
	769	rg(n,2) = random_gauss( iran_part, 5.0_wp )
	770	rg(n,3) = random_gauss( iran_part, 5.0_wp )
	771	ENDDO
	772	ENDDO
[1359]	773
[2417]	774	DO nb = 0, 7
	775	DO n = start_index(nb), end_index(nb)
[1359]	776
[849]	777	!
[2417]	778	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
[2886]	779	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
[2417]	780	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
[849]	781
	782	!
[2417]	783	!-- Calculate the next particle timestep. dt_gap is the time needed to
	784	!-- complete the current LES timestep.
[2886]	785	dt_gap(n) = dt_3d - particles(n)%dt_sum
	786	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
	787	particles(n)%aux1 = lagr_timescale(n)
	788	particles(n)%aux2 = dt_gap(n)
[849]	789	!
[2417]	790	!-- The particle timestep should not be too small in order to prevent
	791	!-- the number of particle timesteps of getting too large
[2886]	792	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap(n) ) THEN
[2417]	793	dt_particle(n) = dt_min_part
	794	ENDIF
[2886]	795	rvar1_temp(n) = particles(n)%rvar1
	796	rvar2_temp(n) = particles(n)%rvar2
	797	rvar3_temp(n) = particles(n)%rvar3
[849]	798	!
[2417]	799	!-- Calculate the SGS velocity components
	800	IF ( particles(n)%age == 0.0_wp ) THEN
[849]	801	!
[2417]	802	!-- For new particles the SGS components are derived from the SGS
	803	!-- TKE. Limit the Gaussian random number to the interval
	804	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
	805	!-- from becoming unrealistically large.
[2886]	806	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	807	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
	808	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	809	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
	810	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	811	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
[849]	812
[2417]	813	ELSE
[849]	814	!
[2417]	815	!-- Restriction of the size of the new timestep: compared to the
	816	!-- previous timestep the increase must not exceed 200%. First,
	817	!-- check if age > age_m, in order to prevent that particles get zero
	818	!-- timestep.
	819	dt_particle_m = MERGE( dt_particle(n), &
	820	particles(n)%age - particles(n)%age_m, &
	821	particles(n)%age - particles(n)%age_m < &
	822	1E-8_wp )
	823	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
	824	dt_particle(n) = 2.0_wp * dt_particle_m
	825	ENDIF
[849]	826
[2417]	827	!-- For old particles the SGS components are correlated with the
	828	!-- values from the previous timestep. Random numbers have also to
	829	!-- be limited (see above).
	830	!-- As negative values for the subgrid TKE are not allowed, the
	831	!-- change of the subgrid TKE with time cannot be smaller than
	832	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
	833	!-- value for the change of TKE
	834	de_dt_min = - e_int(n) / dt_particle(n)
[849]	835
[2417]	836	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
[849]	837
[2417]	838	IF ( de_dt < de_dt_min ) THEN
	839	de_dt = de_dt_min
	840	ENDIF
[849]	841
[2886]	842	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
[2417]	843	de_dx_int(n), de_dt, diss_int(n), &
	844	dt_particle(n), rg(n,1), term_1_2(n) )
[849]	845
[2886]	846	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
[2417]	847	de_dy_int(n), de_dt, diss_int(n), &
	848	dt_particle(n), rg(n,2), term_1_2(n) )
[849]	849
[2886]	850	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
[2417]	851	de_dz_int(n), de_dt, diss_int(n), &
	852	dt_particle(n), rg(n,3), term_1_2(n) )
[849]	853
[2417]	854	ENDIF
[849]	855
[2886]	856	ENDDO
	857	ENDDO
	858	!
	859	!-- Check if the added SGS velocities result in a violation of the CFL-
	860	!-- criterion. If yes choose a smaller timestep based on the new velocities
	861	!-- and calculate SGS velocities again
	862	dz_temp = zw(kp)-zw(kp-1)
	863
	864	DO nb = 0, 7
	865	DO n = start_index(nb), end_index(nb)
	866	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
	867	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
	868	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
	869	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
	870
	871	dt_particle(n) = 0.9_wp * MIN( &
	872	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
	873	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
	874	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
	875
	876	!
	877	!-- Reset temporary SGS velocites to "current" ones
	878	rvar1_temp(n) = particles(n)%rvar1
	879	rvar2_temp(n) = particles(n)%rvar2
	880	rvar3_temp(n) = particles(n)%rvar3
	881
	882	de_dt_min = - e_int(n) / dt_particle(n)
	883
	884	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
	885
	886	IF ( de_dt < de_dt_min ) THEN
	887	de_dt = de_dt_min
	888	ENDIF
	889
	890	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
	891	de_dx_int(n), de_dt, diss_int(n), &
	892	dt_particle(n), rg(n,1), term_1_2(n) )
	893
	894	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
	895	de_dy_int(n), de_dt, diss_int(n), &
	896	dt_particle(n), rg(n,2), term_1_2(n) )
	897
	898	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
	899	de_dz_int(n), de_dt, diss_int(n), &
	900	dt_particle(n), rg(n,3), term_1_2(n) )
	901	ENDIF
	902
	903	!
	904	!-- Update particle velocites
	905	particles(n)%rvar1 = rvar1_temp(n)
	906	particles(n)%rvar2 = rvar2_temp(n)
	907	particles(n)%rvar3 = rvar3_temp(n)
[2417]	908	u_int(n) = u_int(n) + particles(n)%rvar1
	909	v_int(n) = v_int(n) + particles(n)%rvar2
	910	w_int(n) = w_int(n) + particles(n)%rvar3
[849]	911	!
[2417]	912	!-- Store the SGS TKE of the current timelevel which is needed for
	913	!-- for calculating the SGS particle velocities at the next timestep
	914	particles(n)%e_m = e_int(n)
	915	ENDDO
[1359]	916	ENDDO
[2886]	917
[1359]	918	ELSE
[849]	919	!
[1359]	920	!-- If no SGS velocities are used, only the particle timestep has to
	921	!-- be set
	922	dt_particle = dt_3d
[849]	923
[1359]	924	ENDIF
[849]	925
[1359]	926	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
[849]	927
[1359]	928	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
[2417]	929	DO nb = 0, 7
	930	DO n = start_index(nb), end_index(nb)
[1359]	931
[849]	932	!
[2417]	933	!-- Particle advection
	934	IF ( dens_ratio(n) == 0.0_wp ) THEN
[849]	935	!
[2417]	936	!-- Pure passive transport (without particle inertia)
	937	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
	938	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
	939	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
[849]	940
[2417]	941	particles(n)%speed_x = u_int(n)
	942	particles(n)%speed_y = v_int(n)
	943	particles(n)%speed_z = w_int(n)
[849]	944
[2417]	945	ELSE
[849]	946	!
[2417]	947	!-- Transport of particles with inertia
	948	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
	949	dt_particle(n)
	950	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
	951	dt_particle(n)
	952	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
	953	dt_particle(n)
[849]	954
	955	!
[2417]	956	!-- Update of the particle velocity
	957	IF ( cloud_droplets ) THEN
	958	!
	959	!-- Terminal velocity is computed for vertical direction (Rogers et
	960	!-- al., 1993, J. Appl. Meteorol.)
	961	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	962	IF ( diameter <= d0_rog ) THEN
	963	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	964	ELSE
	965	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	966	ENDIF
	967
	968	!
	969	!-- If selected, add random velocities following Soelch and Kaercher
	970	!-- (2010, Q. J. R. Meteorol. Soc.)
	971	IF ( use_sgs_for_particles ) THEN
[2886]	972	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
[3207]	973	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
	974	1.0E-20_wp ) )
[2417]	975	sigma = SQRT( e(kp,jp,ip) )
	976
	977	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	978	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	979	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	980
	981	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	982	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	983	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	984	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	985	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	986	SQRT( 1.0_wp - RL*2 ) sigma * rg3
	987
	988	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	989	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	990	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
	991	ELSE
	992	particles(n)%speed_x = u_int(n)
	993	particles(n)%speed_y = v_int(n)
	994	particles(n)%speed_z = w_int(n) - w_s
	995	ENDIF
	996
	997	ELSE
	998
	999	IF ( use_sgs_for_particles ) THEN
	1000	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1001	exp_term = EXP( -exp_arg * dt_particle(n) )
	1002	ELSE
	1003	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1004	exp_term = particle_groups(particles(n)%group)%exp_term
	1005	ENDIF
	1006	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
	1007	u_int(n) * ( 1.0_wp - exp_term )
	1008	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
	1009	v_int(n) * ( 1.0_wp - exp_term )
	1010	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1011	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
	1012	g / exp_arg ) * ( 1.0_wp - exp_term )
	1013	ENDIF
	1014
	1015	ENDIF
	1016	ENDDO
	1017	ENDDO
	1018
	1019	ELSE
	1020
	1021	DO nb = 0, 7
	1022	DO n = start_index(nb), end_index(nb)
	1023	!
	1024	!-- Transport of particles with inertia
	1025	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
	1026	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
	1027	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
	1028	!
[1359]	1029	!-- Update of the particle velocity
	1030	IF ( cloud_droplets ) THEN
[1822]	1031	!
[2417]	1032	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
	1033	!-- 1993, J. Appl. Meteorol.)
[1822]	1034	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	1035	IF ( diameter <= d0_rog ) THEN
	1036	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	1037	ELSE
	1038	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	1039	ENDIF
[1359]	1040
[1822]	1041	!
	1042	!-- If selected, add random velocities following Soelch and Kaercher
	1043	!-- (2010, Q. J. R. Meteorol. Soc.)
	1044	IF ( use_sgs_for_particles ) THEN
[2886]	1045	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
[3207]	1046	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
	1047	1.0E-20_wp ) )
[2417]	1048	sigma = SQRT( e(kp,jp,ip) )
[1822]	1049
[2417]	1050	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1051	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1052	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
[1822]	1053
[2417]	1054	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	1055	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	1056	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	1057	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	1058	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	1059	SQRT( 1.0_wp - RL*2 ) sigma * rg3
[1822]	1060
[2417]	1061	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	1062	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	1063	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
[1822]	1064	ELSE
[2417]	1065	particles(n)%speed_x = u_int(n)
	1066	particles(n)%speed_y = v_int(n)
	1067	particles(n)%speed_z = w_int(n) - w_s
[1822]	1068	ENDIF
	1069
[1359]	1070	ELSE
[1822]	1071
	1072	IF ( use_sgs_for_particles ) THEN
	1073	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1074	exp_term = EXP( -exp_arg * dt_particle(n) )
	1075	ELSE
	1076	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1077	exp_term = particle_groups(particles(n)%group)%exp_term
	1078	ENDIF
[2417]	1079	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
[1822]	1080	u_int(n) * ( 1.0_wp - exp_term )
[2417]	1081	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
[1822]	1082	v_int(n) * ( 1.0_wp - exp_term )
[2417]	1083	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1084	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
	1085	exp_arg ) * ( 1.0_wp - exp_term )
[1359]	1086	ENDIF
[2417]	1087	ENDDO
[1359]	1088	ENDDO
	1089
[2417]	1090	ENDIF
[1359]	1091
	1092	!
[2417]	1093	!-- Store the old age of the particle ( needed to prevent that a
	1094	!-- particle crosses several PEs during one timestep, and for the
	1095	!-- evaluation of the subgrid particle velocity fluctuations )
	1096	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
	1097
	1098	DO nb = 0, 7
	1099	DO n = start_index(nb), end_index(nb)
[1822]	1100	!
[2417]	1101	!-- Increment the particle age and the total time that the particle
	1102	!-- has advanced within the particle timestep procedure
	1103	particles(n)%age = particles(n)%age + dt_particle(n)
	1104	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
[1359]	1105
[1822]	1106	!
[2417]	1107	!-- Check whether there is still a particle that has not yet completed
	1108	!-- the total LES timestep
	1109	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
	1110	dt_3d_reached_l = .FALSE.
[849]	1111	ENDIF
[1822]	1112
[1359]	1113	ENDDO
[849]	1114	ENDDO
	1115
[1359]	1116	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
[849]	1117
[1929]	1118
[849]	1119	END SUBROUTINE lpm_advec
[1929]	1120
	1121	! Description:
	1122	! ------------
	1123	!> Calculation of subgrid-scale particle speed using the stochastic model
	1124	!> of Weil et al. (2004, JAS, 61, 2877-2887).
	1125	!------------------------------------------------------------------------------!
	1126	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
	1127	dt_n, rg_n, fac )
	1128
	1129	USE kinds
	1130
	1131	USE particle_attributes, &
	1132	ONLY: c_0, sgs_wf_part
	1133
	1134	IMPLICIT NONE
	1135
	1136	REAL(wp) :: a1 !< dummy argument
	1137	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
	1138	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
	1139	REAL(wp) :: diss_n !< dissipation at particle position
	1140	REAL(wp) :: dt_n !< particle timestep
	1141	REAL(wp) :: e_n !< TKE at particle position
	1142	REAL(wp) :: fac !< flag to identify adjacent topography
	1143	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
	1144	REAL(wp) :: rg_n !< random number
	1145	REAL(wp) :: term1 !< memory term
	1146	REAL(wp) :: term2 !< drift correction term
	1147	REAL(wp) :: term3 !< random term
	1148	REAL(wp) :: v_sgs !< subgrid-scale velocity component
	1149
[2100]	1150	!-- At first, limit TKE to a small non-zero number, in order to prevent
	1151	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
	1152	!-- (could occur at the simulation begin).
	1153	e_n = MAX( e_n, 1E-20_wp )
[1929]	1154	!
	1155	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
	1156	!-- multiplied by a flag to switch of both terms near topography.
	1157	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
	1158	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
	1159	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
	1160	!-- disabled if one of the adjacent grid points belongs to topography.
	1161	!-- Moreover, in this case, the previous subgrid-scale component is also set
	1162	!-- to zero.
	1163
	1164	a1 = fs_n * c_0 * diss_n
	1165	!
	1166	!-- Memory term
	1167	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
	1168	* fac
	1169	!
	1170	!-- Drift correction term
	1171	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
	1172	* fac
	1173	!
	1174	!-- Random term
[3241]	1175	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
[1929]	1176	!
	1177	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
	1178	!-- subgrid-scale velocity component is set to zero, in order to prevent a
	1179	!-- velocity build-up.
	1180	!-- This case, set also previous subgrid-scale component to zero.
	1181	v_sgs = v_sgs * fac + term1 + term2 + term3
	1182
	1183	END SUBROUTINE weil_stochastic_eq

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